Question: Rewrite as a simplified fraction. ${1.\overline{12} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 112.1212...\\ 1x &= 1.1212...\end{align*}}$ Subtracting the two equations, we have: ${99x = 111}$ ${x = \dfrac{111}{99}} $ ${x = \dfrac{37}{33}} \text{or} {1 \dfrac{4}{33}}$